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  • Help me answer: - Complex numbers and quadratic equations - JEE Main-6

Let z and w= -5+12i are two complex numbers such that sum of their distances from origin is 18 units then Im\left ( z \right ) satisfies always

  • Option 1)

    -3\leq Im\left ( z \right )\leq 3

  • Option 2)

    -4\leq Im\left ( z \right )\leq 4

  • Option 3)

    -5\leq Im\left ( z \right )\leq 5

  • Option 4)

    -0.6\leq Im\left ( z \right )\leq 0.6

 

Answers (1)

From given condition \left | z \right |+\left | w \right |=18

\left | w \right |=\sqrt{5^{2}+12^{2}}=13\: \Rightarrow \: \left | z \right |=5

\therefore -5\leq Im\left ( z \right )\leq 5

\therefore Option (C)

 

Property of Modulus of z(Complex Number) -

-\left | z \right | \leq Im (z)\leq \left | z \right |

- wherein

Im (z) = Imaginary part of z

|z|= Modulus of z

 

 


Option 1)

-3\leq Im\left ( z \right )\leq 3

This is incorrect

Option 2)

-4\leq Im\left ( z \right )\leq 4

This is incorrect

Option 3)

-5\leq Im\left ( z \right )\leq 5

This is correct

Option 4)

-0.6\leq Im\left ( z \right )\leq 0.6

This is incorrect

Posted by

Vakul

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